Pendulum with a Spring: Analyzing Damping Effects

[Low-Q]

Hi,

I just wonder what happens if a pendulum is attached to a pivot point via a flexible spring, and the spring is:
1 Not damped
2 Partially damped

Will the pendulum stop earlier, or will it sustain as long as a pendulum with no spring attached to it?

Vidar

 

[Low-Q]

Maybe I should add a drawing. Here it is:

 

[Simon Bridge]

Did you try building one to see?

Technically all real-life pendulums can be modeled like this because there is no such thing as a 100% rigid wire. All pendulum strings stretch a bit.

 

[Low-Q]

Did you try building one to see?

Technically all real-life pendulums can be modeled like this because there is no such thing as a 100% rigid wire. All pendulum strings stretch a bit.

I tested this but I could not notice any major difference between them. It should be because the damped spring is actually friction which is energy loss. Maybe I did not damp it enough, because the energy loss should be taken from somewhere. It cannot show up from nothing.

Vidar

 

[Simon Bridge]

Yes it depends on the spring.
You can work out the math - the tension term is replaced with the restoring force of the spring, which will depend on position. Of course if you started with the pendulum not only displaced but it's string stretched by you pulling on it then the bob follows a bouncy path.

In careful classroom experiments, the period of a pendulum gets a bit shorter with increased mass - but if the student is careful with center of mass, they often find the period gets slightly longer with mass. Can you see how?

 

[Low-Q]

Yes it depends on the spring.
You can work out the math - the tension term is replaced with the restoring force of the spring, which will depend on position. Of course if you started with the pendulum not only displaced but it's string stretched by you pulling on it then the bob follows a bouncy path.

In careful classroom experiments, the period of a pendulum gets a bit shorter with increased mass - but if the student is careful with center of mass, they often find the period gets slightly longer with mass. Can you see how?

The change in period will depend on the weight of the pendulum arm itself, wouldn't it? Adding mass at the bottom of a heavy pendulum arm will change the center of mass farther from the hub, so the pendulum period will be longer.

The shorter period would be explained by that the mass you add also have gravity, if there isn't any other obvious reasons for it (??). Like the mass itself have a given extent. In % the extent is greatest between the center of added mass and the hub, moving center of mass slightly upwards, hence shortening the arm and the period.



Vidar

 

[truesearch]

I can agree with Simon Bridge on the practical behaviour.
Whenever I have done this in class it seems it can't make its mind up whether to be a bouncing mass on a spring or a pendulum.
It bounces between the 2.
I have never done any mathematical analysis !

 

[Low-Q]

I can agree with Simon Bridge on the practical behaviour.
Whenever I have done this in class it seems it can't make its mind up whether to be a bouncing mass on a spring or a pendulum.
It bounces between the 2.
I have never done any mathematical analysis !

The pendulum will in this case "manipulate" gravity in terms of alternating the G-force the mass is exposed to depending on the position of the mass during its oscillation back and forth. For this reason the spring will "see" that the mass alters all the time. The spring is stretched most where the G-forces are greatest creating a "pseudo bouncing" effect, even though the bouncing isn't caused directly by the stiffness of the spring and the mass attached to it. Those factors might likely have another longer or shorter period which is the actual bouncing period.

As long the pendulum period is other than the actual bouncing period, there is no way the pendulum period will trigger the bouncing of the relationship between the mass and the spring itself.

So I would say that it is a pendulum with a pseudo bouncing mechanism.

However, if the bouncing period is equal to the pendulum period, we have a double oscillating mechanism making this mechanism both a pendulum and a bouncing mass on a spring.

This is how I see it anyways.

Vidar

 

[Simon Bridge]

The springy pendulum is a kind of coupled oscillator - a mass-on-a-spring and a regular swinging pendulum. The two systems can exchange energy in some setups so you almost alternate between bouncy and swingy motions.

If the coupling is weak you will get one kind of motion dominating.
However, you can usually get smooth motion if you are very careful how you displace the bob. For chaotic motion try driving the pendulum with a random impulse.

Real pendulums also have a torsional oscillation as the bob twists as it moves. It is also difficult to get it to swing exactly in a line so there will be a slight lateral swing as well.
Look up "Border Pendulum".

We usually try to eliminate these extra motions, so the pendulum of a clock has a solid shaft instead of a string and is constrained to move in a line.

I should point out that all masses have gravity - even the wee ones in pendulum experiments. If they didn't, the pendulum would not work. The mass always experiences the same g-force throughout it's motion (given the small scale of the experiment) and does in no sense "manipulate" gravity. You need to get this way of thinking out of your head as it can be highly misleading.

Adding weights to the bottom would, indeed, lower the center of mass (COM) and increase the period of the pendulum but this is an unwieldy setup. It is more usual to add new weights on top of the first one. This raises the COM, lowering the period.

Realizing this, students can be careful to add weights symmetrically, or otherwise adjust the setup, so the COM stays the same. In this case the period increases slightly. How come?

Pendulums are central to physics - you never get away from them.